{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:2ZZHHCAYHQDEWC366XSA7FUGXA","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"5adda8da25b91eabae92e0ed4f03edc7a78a44877f51d5e8f358adba7f47e908","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.CO","submitted_at":"2026-01-30T10:40:22Z","title_canon_sha256":"36fd824a7d0bf6e599dbcb696c13280fc56d5a03bef55953c9be61c2012f757c"},"schema_version":"1.0","source":{"id":"2601.22814","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2601.22814","created_at":"2026-06-10T01:09:54Z"},{"alias_kind":"arxiv_version","alias_value":"2601.22814v2","created_at":"2026-06-10T01:09:54Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2601.22814","created_at":"2026-06-10T01:09:54Z"},{"alias_kind":"pith_short_12","alias_value":"2ZZHHCAYHQDE","created_at":"2026-06-10T01:09:54Z"},{"alias_kind":"pith_short_16","alias_value":"2ZZHHCAYHQDEWC36","created_at":"2026-06-10T01:09:54Z"},{"alias_kind":"pith_short_8","alias_value":"2ZZHHCAY","created_at":"2026-06-10T01:09:54Z"}],"graph_snapshots":[{"event_id":"sha256:774486dee58ab3e034c69d8798b607d236b29b14462c52e988317186406bc354","target":"graph","created_at":"2026-06-10T01:09:54Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2601.22814/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Time-delay embedding is a powerful technique for reconstructing the dynamics of nonlinear systems. However, the reconstruction map is not always an embedding, a condition rarely verified in practice. When the reconstruction map is non-injective, multiple latent states may map to the same reconstructed state, leading to multi-valued $n$-step evolution. Consequently, the induced system no longer admits a deterministic closure, and the dispersion of future trajectories leads to ambiguity. In this work, we establish a measure-theoretic framework to quantify the ambiguity induced by multi-valued ev","authors_text":"Yi Guo, Yiting Duan, Zhikun Zhang","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.CO","submitted_at":"2026-01-30T10:40:22Z","title":"Wasserstein Geometry of Information Loss in Nonlinear Dynamical Systems"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2601.22814","kind":"arxiv","version":2},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:1be5bebeccd722ba6b6b1a1d5c5824f508b20ce443996bdcdba27949d3a6c728","target":"record","created_at":"2026-06-10T01:09:54Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"5adda8da25b91eabae92e0ed4f03edc7a78a44877f51d5e8f358adba7f47e908","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.CO","submitted_at":"2026-01-30T10:40:22Z","title_canon_sha256":"36fd824a7d0bf6e599dbcb696c13280fc56d5a03bef55953c9be61c2012f757c"},"schema_version":"1.0","source":{"id":"2601.22814","kind":"arxiv","version":2}},"canonical_sha256":"d6727388183c064b0b7ef5e40f9686b83dbd2275c2aa2bec66ce483146c042ad","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d6727388183c064b0b7ef5e40f9686b83dbd2275c2aa2bec66ce483146c042ad","first_computed_at":"2026-06-10T01:09:54.120498Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-10T01:09:54.120498Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"l7ULMVe0gHLU2ZAVBCvnpN6lD/YdNcTjYi3AaEmc0nqmjyS1CHwxKPD1SYP/72AgR13vH+aTMs6QnQxJClziBA==","signature_status":"signed_v1","signed_at":"2026-06-10T01:09:54.121470Z","signed_message":"canonical_sha256_bytes"},"source_id":"2601.22814","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1be5bebeccd722ba6b6b1a1d5c5824f508b20ce443996bdcdba27949d3a6c728","sha256:774486dee58ab3e034c69d8798b607d236b29b14462c52e988317186406bc354"],"state_sha256":"9ac25cc69bea1fe7e7ff85914eb9f1bd651acab47e4c16c9fd92c533f05cdcd7"}